The Intrinsic Dimension of Images and Its Impact on Learning

Anonymous

Keywords: Intrinsic Dimension, Sample Complexity

TL;DR: We estimate the intrinsic dimension of practical image datasets and evaluate the impact of intrinsic dimension on sample complexity for learning a good classifier.

Abstract: It is widely believed that natural image data exhibits low-dimensional structure despite being embedded in a high-dimensional pixel space. This idea underlies a common intuition for the success of deep learning and has been exploited for enhanced regularization and adversarial robustness. In this work, we apply dimension estimation tools to popular datasets and investigate the role of low dimensional structure in neural network learning. We find that common natural image datasets indeed have very low intrinsic dimension relative to the high number of pixels in the images. Additionally, we find that low dimensional datasets are easier for neural networks to learn. We validate our findings by carefully-designed experiments to vary the intrinsic dimension of both synthetic and real data and evaluate its impact on sample complexity.

Previous Submission: Yes

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2104.08894/code)